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Output factors and scatter ratios
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 818 (http://iopscience.iop.org/0031-9155/24/4/014) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 159.178.22.27 This content was downloaded on 01/10/2015 at 08:42
Please note that terms and conditions apply.
PHYS. MED. BIOL.,1979, Vol. 24, KO.4, 818-836.
@ 1979
CORRESPONDENCE Output Factors and Scatter Ratios THE EDITOR, Sir, I n their paper, ‘Output Factors and Scatter Ratios for Radiotherapy Units’ (Phys. M e d . Biol., 1978, 23, 968-971), Ahuja, Dubuque and Hendee suggest inclusion of the output factor in the definitions of scatter-air ratio (SAR) and tissue-maximum ratio (TMR). They claim thatthis procedure incorporates scatter from source and collimator in the scatter ratios,provides more accurate definition of these variables, and is essential for accurate dose computations in irregularly shaped fields. I n fact, these authors have based their presentation on what appears to be an incorrectunderstanding of thetraditional definitions. Theirfirsttwo sentences state, ‘Variables such as scatter-air ratios . . . are defined with the implicit assumption that only primary radiation impinges on the patient. That is, radiation scattered from the source and collimator are not considered in the definitions and the dose rate in air is assumed to remain constant with changes in field size.’ These statements are totally incorrect. Traditionally, we define (Johns and Cunningham 1974)
Here, D, is the dose in tissue and D, dose to a small mass of tissue at the same location in air; y is the depth and A the field area. The dose Da(y,A ) in air includes source and collimator scatter and allows both D, and D, to change with field size. All photons in the incident beam before it reaches the phantom are considered primary photons (ICRU 1973). The proposed new definitions are based on the incorrect formulations: and I n fact, D,(y, 0) should be replaced by D,(y, A ) in both these equations. This error results m defining
D,(y, A ) = D,(?/, A ) X [TAR(!/, A )- (1/N)T m ( Y , o)]. (2b) The new definition accomplishes atrivialtransposition of the difference [D,@,A )- D,(y, O ) ] from the primary t o the scattered dose term.
Correspondence
819
It is claimed that this transposition is necessary because, ‘By definition the primary component of dose corresponds to zero field area’, and ‘Because of the output factor, eqn (4) is incorrect asit assumes an exponential decrease in dose in tissue with depth, a condition which is satisfied exactly for only a zero area beam’. Both of the above statements are incorrect. The first, because primary dose D,(y, A ) by definition (eqn ( l a ) )is not confined to A = 0 and the second, because when and if TAR(ZJ, 0) is approximated with exp[ - p(y - dm)]only the primary dose D , and not the tissue dose D , is considered to decrease exponentially with depth. It may be pointed out here that according to theaccepted (1976), definition given by Cunningham (1972) and later adopted by ICRU TAR(Y, 0) is the limit of the function TAR(Y,A)as A ” 0 . Theexponential approximationinitially suggested by Gupta and Cunningham (1966) is unnecessary. If one accepts the view, that a new ‘purist’ approachfor defining the primary is being attempted, such that source and collimator scattered radiation should not be included in the primary dose component, then the new definition of primary Dp(y,A ) = Dp(y,0) = Da(y,0 ) X TAR(Y, 0 ) (3) fails to accomplish thispurpose, unless one assumes (incorrectly) that the source and collimator scatter are zero for zero area fields. I n addition,the proposed definition considers the increase in output withfield size to be entirely due to source and collimator scatter. In fact, with finite size sources, some of this output increase is due to primary radiation from the extended source as the collimator is opened. Practical applications Accuracy of dose calculation The program IRREG (Cunningham, Shrivastava and Wilkinson 1972) calculates dose at a point by the equation
D,(Y,a)= Da(y,A ) X [TAR(Y, 0 ) +=(Y, A ) ] (4) where D, is the dose in tissue and D , dose to a small mass of tissue at thesame location in air, y is the depth and A the field area. is the average integrated scatter-air ratio for irregularly shaped fields. For simplicity, let us consider a cobalt beam of circular field of area A . The accepted definition of Cunningham (1972) gives SAR(Y, A ) = TAR(^, A )- TAR(Y,0). (5) Substituting this in eqn (4)we get
A ) = D a ( y , A )X TAR(Y, A ) which is the correct value of Dt(y,A ) from the definition of TAR. If one used the proposed new definition of SAR, we would write
(6)
Dt(y,A ) = D,(Y, 0) X TAR(Y, 0 )+Da(yt A ) X [TAR(Y, A )-N-l TAR(Y, O)]. (7) Since by definition, N = D,(y,A)/Da(y,0), eqn (7) also reduces to eqn(6)
820
Correspondence
yielding the same value of D&, A ) . Thus, there is no difference in the accuracy of dosimetry calculations by either definition. Eqn (4)is known to yield correct estimates of dose in irregular fields within the accuracy of measurements for Its use, however, all depths y >dm. Eqn (7) does not improveaccuracy. requires knowledge of D&, 0 ) , a quantity quitedifficult to measure accurately. Thetraditionalvariables SAR and TMR form easily tabulated universal functions because they depend only on the medium and beam energy. The source and collimator scatter is approximately accounted for without correcting for degradation of beam energy. Unless the source and collimator scatter is exceptionally degraded in energy and/or forms an unusually large fraction of the t'otal incident radiation, this approximation yields acceptable results. This approximation remains inherent in the new proposed formulations. Eqns (la) and (lb) do not correct for degradation of beam energy due to source and collimator scatter. I n situations where the effective energy of the incident beam changes considerably with field size, these equations only give an approximatedescription of primaryandscattered dose a t depth. I n practice, however, not only are the errors involved small but when using the in TAR(^, 0), ineqn ( l a ) traditional SAR definition (eqn (5)), asmallerror introduces a compensating errorin eqn (lb)so as togive the correct tissue dose when reassembling the components. or The proposed new definitions of SAR and TMR providenotheoretical practical gain. By including the output factor, these variables become machine dependent, requiring individual measurements. Also, measurement of D,(y, 0) becomes necessary. Theinterpolationsrequiredfor this measurement may result in large errors in the more significant primary component D, of the total dose. The above arguments lead to the conclusion that the traditional definitions of variables SAR and TMR should be retained. P. N. SHRIVASTAVA, R. E. SUMMERS, T. V. SAMULSKI,
L. C. BAIRD,
16 November 1978, in final form 21 February 1979
Division of Radiation/Oncology, Allegheny General Hospital, 320 East North Avenue, Pittsburgh, PA 15212, U.S.A.
THE EDITOR, Sir, We appreciatethe efforts of Shrivastava et al. to clarify further our contention that the output fact.or should be incorporated into the definition of variables which describe the scattered radiation component of the total dose delivered to alocation of interestwithinthepatient. I n theirletter,theseauthors outline the conventional approach to defining SAR's and criticise our suggested revisions in this approach, and in the process emphasise the fallacies in the
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My IOPscience
Output factors and scatter ratios
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 818 (http://iopscience.iop.org/0031-9155/24/4/014) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 159.178.22.27 This content was downloaded on 01/10/2015 at 08:42
Please note that terms and conditions apply.
PHYS. MED. BIOL.,1979, Vol. 24, KO.4, 818-836.
@ 1979
CORRESPONDENCE Output Factors and Scatter Ratios THE EDITOR, Sir, I n their paper, ‘Output Factors and Scatter Ratios for Radiotherapy Units’ (Phys. M e d . Biol., 1978, 23, 968-971), Ahuja, Dubuque and Hendee suggest inclusion of the output factor in the definitions of scatter-air ratio (SAR) and tissue-maximum ratio (TMR). They claim thatthis procedure incorporates scatter from source and collimator in the scatter ratios,provides more accurate definition of these variables, and is essential for accurate dose computations in irregularly shaped fields. I n fact, these authors have based their presentation on what appears to be an incorrectunderstanding of thetraditional definitions. Theirfirsttwo sentences state, ‘Variables such as scatter-air ratios . . . are defined with the implicit assumption that only primary radiation impinges on the patient. That is, radiation scattered from the source and collimator are not considered in the definitions and the dose rate in air is assumed to remain constant with changes in field size.’ These statements are totally incorrect. Traditionally, we define (Johns and Cunningham 1974)
Here, D, is the dose in tissue and D, dose to a small mass of tissue at the same location in air; y is the depth and A the field area. The dose Da(y,A ) in air includes source and collimator scatter and allows both D, and D, to change with field size. All photons in the incident beam before it reaches the phantom are considered primary photons (ICRU 1973). The proposed new definitions are based on the incorrect formulations: and I n fact, D,(y, 0) should be replaced by D,(y, A ) in both these equations. This error results m defining
D,(y, A ) = D,(?/, A ) X [TAR(!/, A )- (1/N)T m ( Y , o)]. (2b) The new definition accomplishes atrivialtransposition of the difference [D,@,A )- D,(y, O ) ] from the primary t o the scattered dose term.
Correspondence
819
It is claimed that this transposition is necessary because, ‘By definition the primary component of dose corresponds to zero field area’, and ‘Because of the output factor, eqn (4) is incorrect asit assumes an exponential decrease in dose in tissue with depth, a condition which is satisfied exactly for only a zero area beam’. Both of the above statements are incorrect. The first, because primary dose D,(y, A ) by definition (eqn ( l a ) )is not confined to A = 0 and the second, because when and if TAR(ZJ, 0) is approximated with exp[ - p(y - dm)]only the primary dose D , and not the tissue dose D , is considered to decrease exponentially with depth. It may be pointed out here that according to theaccepted (1976), definition given by Cunningham (1972) and later adopted by ICRU TAR(Y, 0) is the limit of the function TAR(Y,A)as A ” 0 . Theexponential approximationinitially suggested by Gupta and Cunningham (1966) is unnecessary. If one accepts the view, that a new ‘purist’ approachfor defining the primary is being attempted, such that source and collimator scattered radiation should not be included in the primary dose component, then the new definition of primary Dp(y,A ) = Dp(y,0) = Da(y,0 ) X TAR(Y, 0 ) (3) fails to accomplish thispurpose, unless one assumes (incorrectly) that the source and collimator scatter are zero for zero area fields. I n addition,the proposed definition considers the increase in output withfield size to be entirely due to source and collimator scatter. In fact, with finite size sources, some of this output increase is due to primary radiation from the extended source as the collimator is opened. Practical applications Accuracy of dose calculation The program IRREG (Cunningham, Shrivastava and Wilkinson 1972) calculates dose at a point by the equation
D,(Y,a)= Da(y,A ) X [TAR(Y, 0 ) +=(Y, A ) ] (4) where D, is the dose in tissue and D , dose to a small mass of tissue at thesame location in air, y is the depth and A the field area. is the average integrated scatter-air ratio for irregularly shaped fields. For simplicity, let us consider a cobalt beam of circular field of area A . The accepted definition of Cunningham (1972) gives SAR(Y, A ) = TAR(^, A )- TAR(Y,0). (5) Substituting this in eqn (4)we get
A ) = D a ( y , A )X TAR(Y, A ) which is the correct value of Dt(y,A ) from the definition of TAR. If one used the proposed new definition of SAR, we would write
(6)
Dt(y,A ) = D,(Y, 0) X TAR(Y, 0 )+Da(yt A ) X [TAR(Y, A )-N-l TAR(Y, O)]. (7) Since by definition, N = D,(y,A)/Da(y,0), eqn (7) also reduces to eqn(6)
820
Correspondence
yielding the same value of D&, A ) . Thus, there is no difference in the accuracy of dosimetry calculations by either definition. Eqn (4)is known to yield correct estimates of dose in irregular fields within the accuracy of measurements for Its use, however, all depths y >dm. Eqn (7) does not improveaccuracy. requires knowledge of D&, 0 ) , a quantity quitedifficult to measure accurately. Thetraditionalvariables SAR and TMR form easily tabulated universal functions because they depend only on the medium and beam energy. The source and collimator scatter is approximately accounted for without correcting for degradation of beam energy. Unless the source and collimator scatter is exceptionally degraded in energy and/or forms an unusually large fraction of the t'otal incident radiation, this approximation yields acceptable results. This approximation remains inherent in the new proposed formulations. Eqns (la) and (lb) do not correct for degradation of beam energy due to source and collimator scatter. I n situations where the effective energy of the incident beam changes considerably with field size, these equations only give an approximatedescription of primaryandscattered dose a t depth. I n practice, however, not only are the errors involved small but when using the in TAR(^, 0), ineqn ( l a ) traditional SAR definition (eqn (5)), asmallerror introduces a compensating errorin eqn (lb)so as togive the correct tissue dose when reassembling the components. or The proposed new definitions of SAR and TMR providenotheoretical practical gain. By including the output factor, these variables become machine dependent, requiring individual measurements. Also, measurement of D,(y, 0) becomes necessary. Theinterpolationsrequiredfor this measurement may result in large errors in the more significant primary component D, of the total dose. The above arguments lead to the conclusion that the traditional definitions of variables SAR and TMR should be retained. P. N. SHRIVASTAVA, R. E. SUMMERS, T. V. SAMULSKI,
L. C. BAIRD,
16 November 1978, in final form 21 February 1979
Division of Radiation/Oncology, Allegheny General Hospital, 320 East North Avenue, Pittsburgh, PA 15212, U.S.A.
THE EDITOR, Sir, We appreciatethe efforts of Shrivastava et al. to clarify further our contention that the output fact.or should be incorporated into the definition of variables which describe the scattered radiation component of the total dose delivered to alocation of interestwithinthepatient. I n theirletter,theseauthors outline the conventional approach to defining SAR's and criticise our suggested revisions in this approach, and in the process emphasise the fallacies in the
